International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 65-68, Pages 3631-3652
doi:10.1155/S0161171204402026

Shifted quadratic zeta series

Abstract

It is well known that the Riemann Zeta function ς(p)=∑n=1∞1/np can be represented in closed form for p an even integer. We will define a shifted quadratic Zeta series as ∑n=1∞1/(4n2−α2)p. In this paper, we will determine closed-form representations of shifted quadratic Zeta series from a recursion point of view using the Riemann Zeta function. We will also determine closed-form representations of alternating sign shifted quadratic Zeta series.